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Editor's PrefaceVector optimization means minimization or maximization of a vector-valued mapping subject to constraints, or in a more general setting, optimization with ordering cones. In engineering or economics one speaks also of (Edgeworth-) Pareto optimization, multi objective programming or multi criteria decision making.This area of research is growing rapidly. The table of contents of this special issue indicates the present development and actual subjects which can be summarized as follows: 9 the use of the super efficiency concept for a saddle point theory, 9 characterizations of efficient solutions for special problems, 9 9 optimality conditions for nonsmooth problems, 9 an extended duality theory for special problems, 9 numerical methods for the solution of linear and nonlinear problems.Besides these topics further research on a complete optimization theory for set. valued mappings (with applications in stochastic programming and the theory of fuzzy sets) and on numerical methods in the form of expert systems (for the solution of complex problems of optimal design in engineering) can be expected in the future.I am very grateful to the authors for their contributions to this volume, and I am also indebted to the referees for valuable suggestions which have improved the presentation.

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The problem of scheduling identical jobs with chain precedence constraints on two uniform machines is considered. It is shown that the corresponding makespan problem can be solved in linear time.